Does ἐνδεικνύμενος go with ὑμῖν as its object like παρακελευόμενός?With dative it means to show/declare oneself to one.ὅτῳ (ὑμῶν) is governed by ἂν ἀεὶ ἐντυγχάνω, with whomever of you I meet/converse on each occasion.

...I will not stop pursuing knowledge and exhorting you (pl.) and declaring myself to you (pl.),with whomever (sg.) of you I meet/converse on each occasion.

However, the '66 English translation has it simply as "show" with implied accusative "the truth",yet I do not understand why and how he takes ὅτῳ as object of ἐνδείκνυμαι when the case of relative pron. is governed by the verb inside the clause:

...I shall never give up philosophy or stop exhorting you and pointing out the truth to any one of you whom I may meet.

About ὅτῳ, since there's no word that it refers back to, the case that word would have been in is implied, and in this case has to be dative. Or perhaps it's better to say that ὅτῳ ἂν ἀεὶ ἐντυγχάνω ὑμῶν as a whole is a noun clause that is dative, but not marked explicitly as dative. It's like (from the NT) πέντε ἄνδρας εἶχες καὶ νῦν ὃν ἔχεις οὐκ ἔστιν σου ἀνήρ where ὃν is accusative because of its own clause but νῦν ὃν ἔχεις as a whole is nominative.

But I think ὅτῳ ἂν ἀεὶ ἐντυγχάνω ὑμῶν here is sort of an add-on to expand on ὑμῖν and I agree with you that ὑμῖν goes with both παρακελευόμενός and ἐνδεικνύμενος, mostly because of the phrasing, especially the τε καί. I don't think ἐνδεικνύμενος means "show oneself" here. Personally I think the ὅτῳ clause got in the way of what would have been the direct object of παρακελευόμενος and ἐνδεικνύμενος, and it got picked up instead by the λέγων clause which changed the structure of the sentence.